Smears, Iain;
(2026)
On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm.
SMAI Journal of Computational Mathematics
(In press).
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Abstract
For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the error, when considering the numerical solution as the average between the usual continuous piecewise affine-in-time and piecewise constant-in-time reconstructions. This illustrates how the efficiency of the estimators is not only possibly dependent on the choice of norm, but also on the choice of notion of numerical solution.
| Type: | Article |
|---|---|
| Title: | On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10219545 |
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